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In this work, we systematically investigate the mass spectra of fully-heavy hexaquarks within a constituent quark model by including the color Coulomb potential, linear confining potential, and spin-spin interactions. Our results show that all of the fully-heavy hexaquarks lie above the corresponding baryon-baryon thresholds, and thus no stable compact one exists. These states may subsist as resonances and decay into two fully-heavy baryons easily through the fall-apart mechanism, which can be searched in future experiments.

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